An Enhanced Tree-Shaped Adachi-Like Chaotic Neural Network Requiring Linear-Time Computations

Abstract

Abstract. The Adachi Neural Network (AdNN) [1][2][3][4][5], is a fascinating Neural Network (NN) which has been shown to possess chaotic properties, and to also demonstrate Associative Memory (AM) and Pattern Recognition (PR) characteristics. Variants of the AdNN [6,7] have also been used to obtain other PR phenomena, and even blurring. A significant problem associated with the AdNN and its variants, is that all of them require a quadratic number of computations. This is essentially because all their NNs are completely connected graphs. In this paper we consider how the computations can be significantly reduced by merely using a linear number of computations. To do this, we extract from the original complete graph, one of its spanning trees. We then compute the weights for this spanning tree in such a manner that the modified tree-based NN has approximately the same input-output characteristics, and thus the new weights are themselves calculated using a gradient-based algorithm. By a detailed experimental analysis, we show that the new linear-time AdNN-like network possesses chaotic and PR properties for different settings. As far as we know, such a tree-based AdNN has not been reported, and the results given here are novel.

Dynamical Associative Memory: The Properties of the New Weighted Chaotic Adachi Neural Network

“…Anatomists have proved that the topology of a real neural system probably satisfies smallworld and scale-free characteristics [5]- [7]. The pioneering work in regard of modifying CNNs' topology can be found in our previous work [8], [9]. We succeeded in minimizing the computational burden of the AdNN to be linear.…”

Ideal Chaotic Pattern Recognition Is Achievable: The Ideal-M-AdNN - Its Design and Properties

“…We shall now clarify this. As explained in detail in [16,17], if the AdNN weights the external inputs with the quantities determined by a i = 2 + 6x i , the properties of the system become closer to mimicing a PR phenomenon. Adachi et al claimed that such a NN yields the stored pattern at the output periodically, with a short transient phase and a small periodicity.…”